Analytic Deformations Of The Spectrum Of A Family Of Dirac Operators On An Odd Dimensional Manifold With Boundary

Analytic Deformations Of The Spectrum Of A Family Of Dirac Operators On An Odd Dimensional Manifold With Boundary Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Analytic Deformations Of The Spectrum Of A Family Of Dirac Operators On An Odd Dimensional Manifold With Boundary book. This book definitely worth reading, it is an incredibly well-written.

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary

Paul Kirk,Eric Klassen
Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd Dimensional Manifold with Boundary Book PDF

Author : Paul Kirk,Eric Klassen
Publisher : American Mathematical Soc.
Page : 58 pages
File Size : 55,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805381

Get Book

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary by Paul Kirk,Eric Klassen Pdf

The subject of this memoir is the spectrum of a Dirac-type operator on an odd-dimensional manifold M with boundary and, particularly, how this spectrum varies under an analytic perturbation of the operator. Two types of eigenfunctions are considered: first, those satisfying the ``global boundary conditions'' of Atiyah, Patodi, and Singer and second, those which extend to $L^2$ eigenfunctions on M with an infinite collar attached to its boundary. The unifying idea behind the analysis of these two types of spectra is the notion of certain ``eigenvalue-Lagrangians'' in the symplectic space $L^2(\partial M)$, an idea due to Mrowka and Nicolaescu. By studying the dynamics of these Lagrangians, the authors are able to establish that those portions of the two types of spectra which pass through zero behave in essentially the same way (to first non-vanishing order). In certain cases, this leads to topological algorithms for computing spectral flow.

Families of Curves in P^3 and Zeuthen's Problem

Robin Hartshorne
Families of Curves in P 3 and Zeuthen s Problem Book PDF

Author : Robin Hartshorne
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 44,8 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806487

Get Book

Families of Curves in P^3 and Zeuthen's Problem by Robin Hartshorne Pdf

Content Description #"November 1997, volume 130, number 617 (first of 4 numbers)."#On t.p. "P" is blackboard bold.#Includes bibliographical references.

Generalized Symplectic Geometries and the Index of Families of Elliptic Problems

Liviu I. Nicolaescu
Generalized Symplectic Geometries and the Index of Families of Elliptic Problems Book PDF

Author : Liviu I. Nicolaescu
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 51,7 Mb
Release : 1997
Category : Geometry, Differential
ISBN : 9780821806210

Get Book

Generalized Symplectic Geometries and the Index of Families of Elliptic Problems by Liviu I. Nicolaescu Pdf

In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.

Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds

Józef Dodziuk,Jay Jorgenson
Spectral Asymptotics on Degenerating Hyperbolic 3 Manifolds Book PDF

Author : Józef Dodziuk,Jay Jorgenson
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 43,9 Mb
Release : 1998
Category : Asymptotic expansions
ISBN : 9780821808375

Get Book

Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds by Józef Dodziuk,Jay Jorgenson Pdf

In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.

Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains

Valentina Barucci,David E. Dobbs,Marco Fontana
Maximality Properties in Numerical Semigroups and Applications to One Dimensional Analytically Irreducible Local Domains Book PDF

Author : Valentina Barucci,David E. Dobbs,Marco Fontana
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 48,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805442

Get Book

Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains by Valentina Barucci,David E. Dobbs,Marco Fontana Pdf

If $k$ is a field, $T$ an analytic indeterminate over $k$, and $n_1, \ldots, n_h$ are natural numbers, then the semigroup ring $A = k[[T^{n_1}, \ldots, T^{n_h}]]$ is a Noetherian local one-dimensional domain whose integral closure, $k[[T]]$, is a finitely generated $A$-module. There is clearly a close connection between $A$ and the numerical semigroup generated by $n_1, \ldots, n_h$. More generally, let $A$ be a Noetherian local domain which is analytically irreducible and one-dimensional (equivalently, whose integral closure $V$ is a DVR and a finitely generated $A$-module). As noted by Kunz in 1970, some algebraic properties of $A$ such as ``Gorenstein'' can be characterized by using the numerical semigroup of $A$ (i.e., the subset of $N$ consisting of all the images of nonzero elements of $A$ under the valuation associated to $V$ ). This book's main purpose is to deepen the semigroup-theoretic approach in studying rings A of the above kind, thereby enlarging the class of applications well beyond semigroup rings. For this reason, Chapter I is devoted to introducing several new semigroup-theoretic properties which are analogous to various classical ring-theoretic concepts. Then, in Chapter II, the earlier material is applied in systematically studying rings $A$ of the above type. As the authors examine the connections between semigroup-theoretic properties and the correspondingly named ring-theoretic properties, there are some perfect characterizations (symmetric $\Leftrightarrow$ Gorenstein; pseudo-symmetric $\Leftrightarrow$ Kunz, a new class of domains of Cohen-Macaulay type 2). However, some of the semigroup properties (such as ``Arf'' and ``maximal embedding dimension'') do not, by themselves, characterize the corresponding ring properties. To forge such characterizations, one also needs to compare the semigroup- and ring-theoretic notions of ``type''. For this reason, the book introduces and extensively uses ``type sequences'' in both the semigroup and the ring contexts.

Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space

Peter W. Bates,Kening Lu,Chongchun Zeng
Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space Book PDF

Author : Peter W. Bates,Kening Lu,Chongchun Zeng
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 55,8 Mb
Release : 1998
Category : Differentiable dynamical systems
ISBN : 9780821808689

Get Book

Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space by Peter W. Bates,Kening Lu,Chongchun Zeng Pdf

Extends the theory for normally hyperbolic invariant manifolds to infinite dimensional dynamical systems in a Banach space, thereby providing tools for the study of PDE's and other infinite dimensional equations of evolution. In the process, the authors establish the existence of center-unstable and center-stable manifolds in a neighborhood of the unperturbed compact manifold. No index. Annotation copyrighted by Book News, Inc., Portland, OR

$L$ Functions for the Orthogonal Group

David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis
L Functions for the Orthogonal Group Book PDF

Author : David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 55,6 Mb
Release : 1997
Category : Automorphic functions
ISBN : 9780821805435

Get Book

$L$ Functions for the Orthogonal Group by David Ginzburg,Ilya Piatetski-Shapiro,Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro,Stephen Rallis Pdf

In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.

Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable

Kazuyoshi Kiyohara
Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable Book PDF

Author : Kazuyoshi Kiyohara
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 49,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806401

Get Book

Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable by Kazuyoshi Kiyohara Pdf

In this work, two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Michael David Weiner
Bosonic Construction of Vertex Operator Para Algebras from Symplectic Affine Kac Moody Algebras Book PDF

Author : Michael David Weiner
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 43,7 Mb
Release : 1998
Category : Kac-Moody algebras
ISBN : 9780821808665

Get Book

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras by Michael David Weiner Pdf

Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann Zeta-Functions

Christina Q. He,Michel Laurent Lapidus
Generalized Minkowski Content Spectrum of Fractal Drums Fractal Strings and the Riemann Zeta Functions Book PDF

Author : Christina Q. He,Michel Laurent Lapidus
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 52,9 Mb
Release : 1997
Category : Differential equations, Partial
ISBN : 9780821805978

Get Book

Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann Zeta-Functions by Christina Q. He,Michel Laurent Lapidus Pdf

This memoir provides a detailed study of the effect of non power-like irregularities of (the geometry of) the fractal boundary on the spectrum of "fractal drums" (and especially of "fractal strings"). In this work, the authors extend previous results in this area by using the notionof generalized Minkowski content which is defined through some suitable "gauge functions" other than power functions. (This content is used to measure the irregularity (or "fractality") of the boundary of an open set in R]n by evaluating the volume of its small tubular neighborhoods). In the situation when the power function is not the natural "gauge function", this enables the authors to obtain more precise estimates, with a broader potential range of applications than in previous papers of the second author and his collaborators. This text will also be of interest to those working in mathematical physics.

Nonlinear Eigenvalues and Analytic-Hypoellipticity

Ching-Chau Yu
Nonlinear Eigenvalues and Analytic Hypoellipticity Book PDF

Author : Ching-Chau Yu
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 40,7 Mb
Release : 1998
Category : Asymptotic expansions
ISBN : 9780821807842

Get Book

Nonlinear Eigenvalues and Analytic-Hypoellipticity by Ching-Chau Yu Pdf

Explores the failure of analytic-hypoellipticity of two partial differential operators. The operators are sums of squares of real analytic vector fields and satisfy Hormander's condition. By reducing to an ordinary differential operator, the author shows the existence of non-linear eigenvalues, which is used to disprove analytic- hypoellipticity of the original operators. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations

Moshé Flato,Jacques Charles Henri Simon,Erik Taflin
Asymptotic Completeness Global Existence and the Infrared Problem for the Maxwell Dirac Equations Book PDF

Author : Moshé Flato,Jacques Charles Henri Simon,Erik Taflin
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 47,6 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806838

Get Book

Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations by Moshé Flato,Jacques Charles Henri Simon,Erik Taflin Pdf

The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations. These equations govern first quantized electrodynamics and are the starting point for a rigorous formulation of quantum electrodynamics. The presentation is given within the formalism of nonlinear group and Lie algebra representations, i.e. the powerful new approach to nonlinear evolution equations covariant under a group action. The authors prove that the nonlinear Lie algebra representation given by the manifestly covariant Maxwell-Dirac equations is integrable to a global nonlinear representation of the Poincare group on a differentiable manifold of small initial conditions. This solves, in particular, the small-data Cauchy problem for the Maxwell-Dirac equations globally in time. The existence of modified wave operators and asymptotic completeness is proved. The asymptotic representations (at infinite time) turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron are developed.

Lie Groups and Subsemigroups with Surjective Exponential Function

Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Lie Groups and Subsemigroups with Surjective Exponential Function Book PDF

Author : Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 51,7 Mb
Release : 1997
Category : Exponential functions
ISBN : 9780821806418

Get Book

Lie Groups and Subsemigroups with Surjective Exponential Function by Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert Pdf

In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.

The Finite Irreducible Linear 2-Groups of Degree 4

Dane Laurence Flannery
The Finite Irreducible Linear 2 Groups of Degree 4 Book PDF

Author : Dane Laurence Flannery
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 53,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806258

Get Book

The Finite Irreducible Linear 2-Groups of Degree 4 by Dane Laurence Flannery Pdf

This memoir contains a complete classification of the finite irreducible 2-subgroups of $GL(4, {\mathbb C})$. Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.It's features include: a complete classification of a class of $p$-groups; a first step towards extending presently available databases for use in proposed 'soluble quotient algorithms'; and, groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations.

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Algebro Geometric Quasi Periodic Finite Gap Solutions of the Toda and Kac van Moerbeke Hierarchies Book PDF

Author : Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 49,8 Mb
Release : 1998
Category : Evolution equations, Nonlinear
ISBN : 9780821808085

Get Book

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies by Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl Pdf

In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.